iPhone/iPad have pretty awesome cameras and they are pretty awesome displays for photos as well. They’re actually such awesome cameras that almost everyone fills them up with pictures, and then you’re out of space and can’t take any more photos. To see what’s taking up space navigate to a breakdown of what’s taking up space and how much.
Go to Settings > General > Storage & iCloud Usage. Under the heading of Storage you’ll see Used (what’s actually taken up on your phone) and Available (how much free space you have). There is another option, Manage Storage, which gives you a breakdown of how much space each app is taking up as well as the option to remove that app and its data right from there.
Photos & Camera is the number one culprit for taking up space on most of the phones I see. It’s just so easy to take photos like crazy and run out of space. The biggest culprit is videos; a short video can take up more space than a few dozen photos, or maybe even a hundred or more, depending on the length of the video.
There are a number of different storage options solutions. A common one is to move them onto your computer and remove them from your iPhone. Another one is to upload them to an online service like Backblaze (cheaper than iCloud unlimited storage for $5.00/month) or use iCloud Photo Library. You may need to pay for extra iCloud storage space, but $0.99 per month gets 50GB. It can take hours or even days to upload an entire Photo Library, depending on the size and the upload speed, but it’s really great when it all gets uploaded. There are two options: Optimize iPhone Storage, meaning you get a low resolution thumbnail on the device and a full version available to download in iCloud, and when you try to view that photo it will download for your viewing. The other is Download and Keep Originals. I do that on my Mac, where I have a ton of available space, but not on my phone.
No matter which solution you use remember that if your iPad or iPhone is having a problem one of the "fixes" is to restore the device to factory settings. That means ALL YOUR PICTURES and contacts, videos etc, get erased. Get into the habit of backing up, whether to your computer or an online service.